X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FRNG024-7.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FRNG024-7.p.ma;h=b4d302383c9fd536f6127d9b17ca8c07cdcc87ae;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/RNG024-7.p.ma b/matita/tests/TPTP/Veloci/RNG024-7.p.ma new file mode 100644 index 000000000..b4d302383 --- /dev/null +++ b/matita/tests/TPTP/Veloci/RNG024-7.p.ma @@ -0,0 +1,99 @@ + +include "logic/equality.ma". +(* Inclusion of: RNG024-7.p *) +(* -------------------------------------------------------------------------- *) +(* File : RNG024-7 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Ring Theory (Alternative) *) +(* Problem : Right alternative *) +(* Version : [Ste87] (equality) axioms : Augmented. *) +(* Theorem formulation : In terms of associators *) +(* English : *) +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) +(* : [Ste92] Stevens (1992), Unpublished Note *) +(* Source : [TPTP] *) +(* Names : *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *) +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *) +(* Number of atoms : 23 ( 23 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 8 ( 3 constant; 0-3 arity) *) +(* Number of variables : 45 ( 2 singleton) *) +(* Maximal term depth : 5 ( 3 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include nonassociative ring axioms *) +(* Inclusion of: Axioms/RNG003-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : RNG003-0 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Ring Theory (Alternative) *) +(* Axioms : Alternative ring theory (equality) axioms *) +(* Version : [Ste87] (equality) axioms. *) +(* English : *) +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) +(* Source : [Ste87] *) +(* Names : *) +(* Status : *) +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) +(* Number of literals : 15 ( 15 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) +(* Number of variables : 27 ( 2 singleton) *) +(* Maximal term depth : 5 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----There exists an additive identity element *) +(* ----Multiplicative zero *) +(* ----Existence of left additive additive_inverse *) +(* ----Inverse of additive_inverse of X is X *) +(* ----Distributive property of product over sum *) +(* ----Commutativity for addition *) +(* ----Associativity for addition *) +(* ----Right alternative law *) +(* ----Left alternative law *) +(* ----Associator *) +(* ----Commutator *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* ----The next 7 clause are extra lemmas which Stevens found useful *) +theorem prove_right_alternative: + \forall Univ:Set. +\forall add:\forall _:Univ.\forall _:Univ.Univ. +\forall additive_identity:Univ. +\forall additive_inverse:\forall _:Univ.Univ. +\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ. +\forall commutator:\forall _:Univ.\forall _:Univ.Univ. +\forall multiply:\forall _:Univ.\forall _:Univ.Univ. +\forall x:Univ. +\forall y:Univ. +\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))). +\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))). +\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))). +\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). +\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). +\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). +\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y). +\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X). +\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +\forall H15:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +\forall H17:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +\forall H18:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity. +\forall H19:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity. +\forall H20:\forall X:Univ.eq Univ (add X additive_identity) X. +\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)